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Robustness in the volume-to-point heat conduction optimization problem

机译：体积到点导热优化问题的鲁棒性

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摘要

This paper deals with the systematic and quantitative robustness analysis of solutions to the volume-to-point (VP) heat conduction optimization problem, including solutions by constructal theory (CT), bionic optimization (BO), simulated annealing (SA) as well as random solutions. The impacts of both load-induced and random failures are examined. All the solutions behave similarly during a failure. A tiny high-heat-flux-induced failure causes huge performance loss, which is the worst possible case. While the best case is a failure at positions of low heat flux, a large amount of which only causes a small performance loss. Random failure generally results in a loss roughly linear with failure amount, but sudden loss increase happens. Both intuitive and practical definitions of robustness are considered. Intuitively, a performance-robustness trade-off is seen for all the solutions, with poorer solutions being robuster. Practically things are different, with SA solutions both the best in performance and the robustest during a failure in the worst case. However, CT and BO solutions turn out to be robuster than SA solution in the best case, and CT solution may be more preferable in practice due to its regular geometry. With robustness taken into consideration, different solutions could be evaluated more comprehensively, the critical aspects concerning the practical realization of the solutions are also revealed, and furthermore the significance of robustness analysis in general VP problems is accentuated.
机译：本文针对体积到点（VP）导热优化问题的解决方案进行系统和定量的鲁棒性分析，包括构造理论（CT），仿生优化（BO），模拟退火（SA）以及随机解。研究了负载引起的故障和随机故障的影响。在故障期间，所有解决方案的行为都相似。微小的由高热通量引起的故障会导致巨大的性能损失，这是最糟糕的情况。虽然最好的情况是在低热通量的位置发生故障，但大量故障只会造成很小的性能损失。随机故障通常会导致损失与故障量大致成线性关系，但是会突然发生损失增加。健壮性的直观定义和实际定义都被考虑了。凭直觉，所有解决方案都可以在性能-鲁棒性之间进行权衡，而较差的解决方案则更鲁棒。实际上，情况有所不同，SA解决方案不仅性能最佳，而且在最坏的情况下在发生故障时也最强大。但是，在最佳情况下，CT和BO解决方案比SA解决方案更强大，而CT解决方案由于其规则的几何形状在实践中可能更可取。考虑到鲁棒性，可以更全面地评估不同的解决方案，还揭示了有关解决方案实际实现的关键方面，此外，还强调了鲁棒性分析在一般VP问题中的重要性。

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